# How do you solve #abs(3x-4)<=x#?

##### 3 Answers

or

#### Explanation:

2 cases

or

If

Or

If

Or

Notice that

Then

#### Explanation:

Here's one method...

Given:

#abs(3x-4) <= x#

Note in passing that

Given that

#9x^2-24x+16 <= x^2#

Subtract

#8x^2-24x+16 <= 0#

Divide both sides by

#x^2-3x+2 <= 0#

Factorise the quadratic to find:

#(x-1)(x-2) <= 0#

So this is a parabola with positive

Hence the solution of our inequality is:

#1 <= x <= 2#

In interval notation:

#x in [1, 2]#

#### Explanation:

graph{(|3x-4|-x-y)<=0 [-5, 5, -2.5, 2.5]}